It is state of the art to use two Hall generators whose Hall voltages are subtracted from each other in order to measure the gradients of magnetic leakage fields in the non-destructive materials testing of materials by the leakage-flux method. The two Hall generators are arranged in parallel to each other in two different planes and overlap each other to some extent. The broad sides of the Hall generators are aligned at a small distance from the surface of the ferromagnetic body to be tested (U.S. Pat. No. 3,710,236). With this known arrangement, grain structure faults can be registered that are contained at least to some extent in one plane that passes vertically to the broad sides of the Hall generators and parallel to planes placed through the connecting points of the Hall electrodes.